The diagram below summarises three major steps and equipment (or 'machines') for the steel-making process of a Japanese company (as presented in Zweben & Fox, Chapter 21). From The Blast Furnace Converter #1 Converter #2 Converter #3 Refinement equipment #1 Refinement equipment #2 Refinement equipment #8 Refinement equipment #9 Continuous caster #1 Continuous caster #2 Continuous caster #3 Continuous caster #4 Continuous caster #5 To The Rolling The converter refines pig iron into steel of required composition, the refinement equipment removes impurities from molten steel and/or adds alloy ingredients on molten steel to make high-grade steel, and a continuous caster casts molten steel into slabs, blooms or billets. Assume that this production plant has three identical converters, nine different refining devices which are assigned according to the grade of the product, and five different continuous casters which are assigned according to the specification of the product. There is a fixed number of charges that should be scheduled for production in a day (A charge is a work unit representing a fixed amount of molten steel).